Module 2.4

Creating and Solving Inequalities

How do you write and solve an inequalitythat represents a real-world situation?

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𝒙 < 𝟒

𝒙 + 𝟔 > 𝟏𝟒

𝟓𝒙 − 𝟔 ≤ 𝟑𝟗

Examples:

Inequalities are solved just like equations, by performing inverse

operations.

𝒙 + 𝟔 > 𝟏𝟒 𝟓𝒙 − 𝟔 ≤ 𝟑𝟗 𝟑 𝒙 − 𝟐 ≥ −𝟑

If necessary, first do a distribution (to eliminate the

parenthesis). The variable can appear on

both sides.

RULE: The inequality sign must be reversed when multiplying or dividing both sides of an inequality by a negative number.

−𝟏

𝟐𝒙 > 𝟒

You have probably seen a sign at an amusement park saying something like, “You must be at least 48 inches tall to ride this ride.” This statement could be written as h ≥ 48 in., where h represents the height of a person allowed to ride.

Phrases

At most, No more than, Up to, Maximum

At least, No less than, Down to, Minimum

P. 74

Nora is planning a birthday party for her little sister, Colleen. Nora’s budget will allow her to spend no more than $50 for party supplies. Eight children, including Colleen, will attend the party, and Nora wants to determine how much she could spend on party favors for each child. She will also purchase a cake for $10. Write an inequality that represents the situation, and find possible solutions.

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The solution set of an inequality consists of all values that make the statement true. Describe the whole dollar amounts that are in the solution set for this situation.

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